Suppose two independent calims are made on two insured homes, where each claim has pdf f(x)=4/x^5, 1< x < infinity, in which the unity is $1000. Find the expected value of the largest claim.

Here was my approach:

Integrate f(x) to get F(x)=-x^-4

Apply the order statistics max equation: n{[Fn]^n-1}*f(x) which should have given me: 2(-x^-4)4/x^5. I won't post the computation since the answer is wrong.

Here is the solution:

P(X<t) = P(max(x1,x2)<t) ... (i)

= P(x1<t, x2<t) ... (ii)

= double integral of fx1,x2(x,y) dx dy (both integrals from -infinity to t) ... (iii)

= (1-1/t^4)^2, t>1 (iv)

What I don't get is step (iii) and (iv). How does one go from (ii) to (iii) and then from (iii) to (iv)?

The rest of the problem is pretty simple. You just plug in the result of P(x<t) into the order statistics min equations and then just take the expected value of that. You end up getting 32/21 for those that care.

Thanks in advance!